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I created a truth table with three inputs and randomly select high outputs so that I could practice doing boolean algebra. I've been able to answer some I've seen on the internet, but have failed when I just made up my own example to practice with. I've included a picture to see how far I got and ultimately where I've not been able to move past.

I have my rules cheat sheet beside me, but I'm going nowhere fast.

It has been about 30 years since I attempted any boolean algebra or Karnaugh mapping, so please take my limited advice with a grain of salt, but I think that you might be able to leave the first term alone and factor /C out of the second and third terms, ending up with /A/BC + /CA. Going back to your strategy, /AB + A/B can be reduced to A XOR B, but I don't know if introducing XOR into the mix is in line with what you are asking.

Mike B.

That's for the reply Mike.

I haven't tried what you mentioned yet, but I'm going to rework it as you suggested in the morning. However, I know of XOR, it's truth table and the gate symbol. When I went to reduce the term in the picture, I didn't immediately recognized that A~C + ~AC was an XOR until I plugged in a truth table. I was trying to factor out and reduce, but the example in the picture I fail to see what I'm missing. Does that mean you can go to factor out a term, but the resulting expression cannot be reduced? Given all the examples I've worked before, I just assume that every time you factor you can reduce. It doesn't appear so in that example.

The way you should factor this is not via the first two terms, but the first and the third:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + AB/C

If you're going to practice doing this by hand, you should take a look at Karnaugh maps (e.g, https://en.wikipedia.org/wiki/Karnaugh_map)

There is a minor error in this:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + AB/C

It should be:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + /A/BC

This truth table is a good example of logic that does not reduce to simple terms.

Daryl

Argh. Yes. It should be the same as the result that barrym got, and I thought I checked that... clearly not.

If you combine the bottom two terms, the B's cancel.
That is about the most I see.
The problems you may find are often like the math problems you get in grammar school.
You see problems like 24 / 3 but rarely 26 / 3.
Dwight

Thanks for everyone that replied.

What does the underline represent?

If I'm understanding this correctly, I just happened to make up an example that was a little complex.

it was the best way for me to point out what part was wrong... it has nothing to do with logic representation.

Yes, sometimes you get lucky and your truth table will reduce to something simple...but more often than not (for me), I end up with something that is not much simpler than the original equation.

Daryl